Yasuo Ezawa

CHARGE WAVEFORM OF A NEW TWO-DIMENSIONAL POSITION-SENSITIVE SILICON DETECTOR.

The operation principles of the two-dimensional position-sensitive silicon detector newly developed by Doke et al. were studied using a simple model. This model treats the detector as an area of continuously distributed capacitance C and resistance Rs of position surface layer. A linear relationship can then be obtained between the position of the incident particle and change collected at the contacts of the detector. The kinetics of charge collected at corner contacts, ballistic deficit and noise were calculated. Rise time of the charge pulse (10–90%) was found to vary with the position of incidence up to about RsC/8. It was found that a shaping time constant longer than RsC/3 is required for pulse shaping with single CR-differentiation and single CR-integration in order to obtain a ballistic deficit of less than 1%.

Third quantization of f(R)-type gravity

We examine the third quantization of f(R)-type gravity, based on its effective Lagrangian in the case of a flat Friedmann–Lemaitre–Robertson–Walker metric. Starting from the effective Lagrangian, we make a suitable change of variable and the second quantization, and we obtain the Wheeler–DeWitt equation. The third quantization of this theory has been considered. The uncertainty relation of the universe has been investigated in the example of f(R)-type gravity, where f(R) = R2. It has been shown that, at late times namely the scale factor of the universe is large, the spacetime does not contradict to become classical, and, at early times namely the scale factor of the universe is small, the quantum effects dominate.

Third quantization of

In the previous paper, we examined the third quantization of the f(R)-type gravity and studied the Heisenberg uncertainty relation of the universe in the example of f(R) = R2. In this work, the Heisenberg uncertainty relation of the universe is investigated in the general f(R)-type gravity where tachyonic states are avoided. It is shown that, at late times namely the scale factor of the universe is large, the spacetime becomes classical, and, at early times namely the scale factor of the universe is small, the quantum effects dominate.

f(R)

In the previous paper, we examined the third quantization of the f(R)-type gravity and studied the Heisenberg uncertainty relation of the universe in the example of f(R) = R2. In this work, the Heisenberg uncertainty relation of the universe is investigated in the general f(R)-type gravity where tachyonic states are avoided. It is shown that, at late times namely the scale factor of the universe is large, the spacetime becomes classical, and, at early times namely the scale factor of the universe is small, the quantum effects dominate.

-type gravity II - General

Following the method of Buchbinder and Lyakhovich, we carry out a canonical formalism for a higher-curvature gravity theory in which the Lagrangian density is given in terms of a function of the scalar curvature as , where f is a nonlinear differentiable function of . We comment on the physical significance of the metric taking the Robertson-Walker metric as an example.

f(R)

In this paper, we analyse the Wheeler-DeWitt equation in the third quantized formalism. We will demonstrate that for certain operator ordering, the early stages of the universe are dominated by quantum fluctuations, and the universe becomes classical at later stages during the cosmic expansion. This is physically expected, if the universe is formed from quantum fluctuations in the third quantized formalism. So, we will argue that this physical requirement can be used to constrain the form of the operator ordering chosen. We will explicitly demonstrate this to be the case for two different cosmological models.

case

We propose a canonical formalism of f(R)-type gravity using a set of phase variables which is partly different from that used in the formalism of Buchbinder and Lyakhovich (BL). The new coordinates corresponding to the time derivatives of the metric are taken to be the Lie derivatives of the metric, which is the same as in BL. The momenta canonically conjugate to the new coordinates and Hamiltonian density are defined similarly to the formalism of Ostrogradski. It is shown that, in our formalism, the Hamiltonian is invariant under the change of the original coordinates, which is not the case in the formalism of BL.A canonical formalism of f(R)-type gravity is proposed, resolving the problem in the formalism of Buchbinder and Lyakhovich(BL). The new coordinates corresponding to the time derivatives of the metric are taken to be its Lie derivatives which is the same as in BL. The momenta canonically conjugate to them and Hamiltonian density are defined similarly to the formalism of Ostrogradski. It is shown that our method surely resolves the problem of BL.

Third quantization of

We extend the improved Milnes (Milne-spline) method for obtaining eigenvalues and eigenfunctions to the cases of long-range and singular potentials, for which we have conjectured that it is difficult to apply the method. Contrary to our conjecture it turned out that the method is valid also for Coulomb potential and repulsive 1/xn(n = 2,3,...) type potential. Further we applied the method for two cases, for which the solutions are not known, in order to investigate the stability of the multi-dimensional universe. It has been shown that the extra-dimensional (internal) space of our universe is not stable in classical Einstein gravity as well as canonically quantized one. Two possibilities for stabilization were investigated: (i) noncanonically quantized Einstein gravity and (ii) canonically quantized higher curvature gravity. It has been suggested that the space is stable by qualitative and approximate methods. Exact analytical treatment is very difficult, so that numerical investigation is highly desirable. Numerical investigation shows that the space is stable with sufficient reliability.

f(R)

We present a canonical formalism of the f(R)-type gravity using the Lie derivatives instead of the time derivatives by refining the formalism of our group. The previous formalism is a direct generalization of the Ostrogradski’s formalism. However the use of the Lie derivatives was not sufficient, in that Lie derivatives and time derivatives are used in a mixed way, so that the expressions are somewhat complicated. In this paper, we use the Lie derivatives and foliation structure of the spacetime thoroughly, which makes the procedure and the expressions far more concise.

-type gravity II

The stability of the extra-dimensional spaces in higher-curvature gravity theories is investigated using the semiclassical approximation to the Wheeler-DeWitt equation. It is shown that, if there exists only one internal space, the space is stable under a certain condition.